document.write( "Question 1163264: A triangular prism of cheese is measured and found to be 3 inches tall. The edges of its base are 9, 9, and 4 inches long. Several congruent prisms are to be arranged around a common 3-inch segment. How many prisms can be accommodated? To the nearest cubic inch, what is their total volume? \n" ); document.write( "

Algebra.Com's Answer #787305 by ikleyn(52794) $\"\"$ $\"About$

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document.write( "The triangle (9,9,4) is an isosceles triangle.\r\n" );
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document.write( "Let \"a\" be its angle opposite to the base of \"4\".\r\n" );
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document.write( "Then   = ;   =  = 0.2241 radians.\r\n" );
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document.write( "Hence, the angle  \"a\"  is  a = 2*0.2241 = 0.4482.\r\n" );
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document.write( "The number of such angles in full angle of   radians is   =  = 14.012,\r\n" );
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document.write( "or approximately 14.\r\n" );
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document.write( "Hence, the answer to the first question is 14 prisms.\r\n" );
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document.write( "Next, to find the volume of one such a prism, find first the area of its base.\r\n" );
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document.write( "To find the area of the  (9,9,4)-triangle, use the Heron's formula.\r\n" );
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document.write( "Semi-perimeter is  s =  =  = 11;\r\n" );
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document.write( "hence, the area is  A =  =  =  = 17.55 cubic inches.\r\n" );
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document.write( "The volume of one prism = 3*17.55 = 52.65 cubic inches,\r\n" );
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document.write( "and the volume of the 14 prisms is  14*52.65 = 737 cubic inches.    ANSWER\r\n" );
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